Question

A parallel beam of monochromatic light is used in a Young’s double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. Slow that if the incident beam makes an angle

θ=sin-1 λ2dwith the normal to the plane of the slits, there will be a dark fringe at the centre P0 of the pattern.

Answer 1

It can be seen from the figure that the wavefronts reaching O from S1 and S2 will have a path difference of S2X. As the path difference is an odd multiple of λ/2, there will be a dark fringe at point P0.

Answer 2

Explanation:

Let the two slits are S1 and S2 with separation d as shown in the attached figure.

It can be seen from the figure that the wavefronts reaching O from S1 and S2 will have a path difference of S2X

In ΔS1S2X

sinθ= S2X/S1S2

So path difference =S2X=S1S2 sinθ= d sinθ

=d x λ/2d =λ/2

As the path difference is an odd multiple of λ/2 there will be dark fringe at a point p.